Revisiting the dynamics of finite-sized satellite near the planet in ER3BP

TL;DR

This paper introduces a semi-analytical method to analyze the motion of finite-sized, nearly spherical satellites in the elliptic restricted three-body problem, focusing on their quasi-stable, trapped motion near the secondary planet.

Contribution

It revisits and updates previous approaches to satellite dynamics in ER3BP, incorporating a novel gravitational potential model for solid ellipsoid satellites.

Findings

Demonstrates quasi-stable trapped motion near the secondary planet.

Provides a semi-analytical framework for satellite motion analysis.

Enhances understanding of satellite dynamics in elliptic three-body systems.

Abstract

A novel approach for solving equations of motion of finite-sized satellite supposed to be moving in a proximity and around the planet in the elliptic restricted three-body problem, ER3BP is presented in this semi-analytical investigation. We consider two primaries, M_Sun and m_planet (the last is secondary in that binary system), both are orbiting around their barycenter on elliptic orbits. Satellite is considered to be the solid ellipsoid having nearly spherical form, with its gravitational potential to be given by a formula of MacCullagh type. Our aim is to revisit previously presented in work [Ashenberg, 1996] approach and to investigate the updated type of the satellite dynamics correlated implicitly to a kind of trapped motion (in the synodic co-rotating Cartesian coordinate system) in so way that satellite will always to be located near the secondary planet, m_planet, moving on quasi-stable elliptic orbit.